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Nilai x yang memenuhi ∣∣x∣+2x∣≤3 adalah ...

Pertanyaan

Nilai x yang memenuhi open vertical bar open vertical bar x close vertical bar plus 2 x close vertical bar less or equal than 3 adalah ...

  1. negative 3 less or equal than x less or equal than 3 

  2. negative 1 less or equal than x less or equal than 1

  3. x less or equal than 2 

  4. x less or equal than 0 

  5. x greater or equal than 0 

S. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

tidak ada jawaban yang tepat dari opsi pada soal.

Pembahasan

Ingat bahwa:

Jika open vertical bar f left parenthesis x right parenthesis close vertical bar less or equal than a maka negative a less or equal than f left parenthesis x right parenthesis less or equal than a.

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar open vertical bar x close vertical bar plus 2 x close vertical bar end cell less or equal than 3 row cell negative 3 end cell less or equal than cell open vertical bar x close vertical bar plus 2 x less or equal than 3 end cell row blank blank blank row cell negative 3 end cell less or equal than cell open vertical bar x close vertical bar plus 2 x end cell row cell negative 3 minus 2 x end cell less or equal than cell open vertical bar x close vertical bar end cell row blank blank dan row cell open vertical bar x close vertical bar plus 2 straight x end cell less or equal than 3 row cell open vertical bar straight x close vertical bar end cell less or equal than cell 3 minus 2 straight x end cell end table

Berdasarkan perhitungan di atas diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x close vertical bar end cell greater or equal than cell negative 3 minus 2 x end cell row x less or equal than cell 3 plus 2 x end cell row cell x minus 2 x end cell less or equal than 3 row cell negative x end cell less or equal than 3 row x greater or equal than cell negative 3 end cell row blank blank atau row x greater or equal than cell negative 3 minus 2 x end cell row cell x plus 2 x end cell greater or equal than cell negative 3 end cell row cell 3 x end cell greater or equal than cell negative 3 end cell row x greater or equal than cell negative 1 end cell end table        dan        table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x close vertical bar end cell less or equal than cell 3 minus 2 x end cell row x greater or equal than cell negative 3 plus 2 x end cell row cell x minus 2 x end cell greater or equal than cell negative 3 end cell row cell negative x end cell greater or equal than cell negative 3 end cell row x less or equal than 3 row blank blank atau row x less or equal than cell 3 minus 2 x end cell row cell x plus 2 x end cell less or equal than 3 row cell 3 x end cell less or equal than 3 row x less or equal than 1 end table

Lakukan uji titik untuk melihat daerah penyelesaian pertidaksamaan tersebut.

Misal x equals negative 4

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar open vertical bar negative 4 close vertical bar plus 2 left parenthesis negative 4 right parenthesis close vertical bar end cell less or equal than 3 row cell open vertical bar 4 minus 8 close vertical bar end cell less or equal than 3 row 4 less or equal than cell 3 horizontal ellipsis open parentheses salah close parentheses end cell end table

Misal x equals negative 2

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar open vertical bar negative 2 close vertical bar plus 2 left parenthesis negative 2 right parenthesis close vertical bar end cell less or equal than 3 row cell open vertical bar 2 minus 4 close vertical bar end cell less or equal than 3 row 2 less or equal than cell 3 horizontal ellipsis open parentheses benar close parentheses end cell end table

Misal x equals 0

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar open vertical bar 0 close vertical bar plus 2 left parenthesis 0 right parenthesis close vertical bar end cell less or equal than 3 row cell open vertical bar 0 plus 0 close vertical bar end cell less or equal than 3 row 0 less or equal than cell 3 horizontal ellipsis open parentheses benar close parentheses end cell end table

Misal x equals 2

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar open vertical bar 2 close vertical bar plus 2 left parenthesis 2 right parenthesis close vertical bar end cell less or equal than 3 row cell open vertical bar 2 plus 4 close vertical bar end cell less or equal than 3 row 6 less or equal than cell 3 horizontal ellipsis open parentheses salah close parentheses end cell end table

Berdasarkan uji titik tersebut diperoleh nilai x yang memenuhi pertidaksamaan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open vertical bar open vertical bar x close vertical bar plus 2 x close vertical bar end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank less or equal than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table adalah negative 3 less or equal than x less or equal than 1.

Jadi, tidak ada jawaban yang tepat dari opsi pada soal.

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